COMSOL - Topology Optimization of an Actively Cooled … · 2015. 11. 20. · •The topology...

Topology Optimization of an Actively Cooled Electronics Section for Downhole Tools

S. Soprani*, J. H. K. Haertel, B. S. Lazarov, O. Sigmund, K. Engelbrecht

27 November 2014DTU Energy, Technical University of Denmark

Table of contents

• Introduction

• Method and COMSOL model

• Analysis of the results

• Choice of the final design

• Conclusions

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Introduction

• Topology Optimization: mathematical approach that optimizes thematerial layout within a given design space and boundary conditions.

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• Downhole Tool: cylindrical robotic tool used to increase or restore theproduction of oil and gas wells (well cleaning, pipe cutting, installation ofvalves).

Introduction

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TEC - Thermoelectric (Peltier) cooler:

upgrade the maximum operating temperature from175°C to 200 °C.

Q

Ifeed


Problem formulation

5

Metallic housing

(o.d. 80mm)

Structural chassis

(o.d. 60mm)

Optimizable chassis

T-sensitiveelectronics

(PCB)

TEC Heat spreader + soft thermal pad

Optimize the distribution of aluminum-thermal insulation within the chassis

Minimize the average PCB temperature

Design Criteria:

• Use aluminum to enhancethe cooler’s heat rejectionto the well.

• Use thermal insulation toprotect the cooledelectronics.

Axial section of the downholetool’s implemented geometry.

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Governing equations

6

• Heat conduction 𝛻 −𝑘𝛻𝑇 = 𝑄𝑠𝑜𝑢𝑟𝑐𝑒 (1)

• Modified heat conduction 𝛻 𝑱𝑆𝑇 − 𝑘𝛻𝑇 = 𝑄𝐽𝑜𝑢𝑙𝑒𝐻𝑒𝑎𝑡𝑖𝑛𝑔 (2)

Boundary conditions

Convective heat flux (Tfluid, h)

Thermal insulation

Heat source(1 W)

TEC feed current Ifeed

Thermal (contact) resistance

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𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒: 𝑓𝑜𝑏𝑗 𝑇, 𝜌𝑑𝑒𝑠𝑖𝑔𝑛 =1

𝐴𝑃𝐶𝐵 𝛺𝑃𝐶𝐵

𝑇 𝑑𝛺𝑃𝐶𝐵 (3)

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Topology Optimization Implementation(SIMP method)

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𝑖𝑛𝑡𝑒𝑟𝑝𝑜𝑙𝑎𝑡𝑖𝑜𝑛 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝑘𝑆𝐼𝑀𝑃= 𝑘𝑖𝑛𝑠 + 𝑘𝐴𝑙 − 𝑘𝑖𝑛𝑠 𝜌p (5)

𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠: 0 ≤ 𝜌𝑑𝑒𝑠𝑖𝑔𝑛 ≤ 1 (4)

ρdesignDensity filter

f(r) 𝜌 Projection function

p(η,β) 𝜌

27 November 2014DTU Energy, Technical University of Denmark8

Simulation results

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p(η,β = 1)

p(η,β = 8)

Ifeed = 4 A h = 50 Wm-2K-1


Simulation results

9

Tfluid = 200 °C h = 25, 50, 100, 500 Wm-2K-1 Ifeed = 1, 2, 3, 4 A

• Low Ifeed / High h

• Aluminum pad length grows with Ifeed and decreases with h.

• High Ifeed / Low h

• Aluminum layer thickness grows with Ifeed and decreases with h.

Aluminum

Insulator

𝜌 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛Ifeed = 2 A h = 100 Wm-2K-1

Design 1

𝜌 𝑜𝑝𝑡𝑖𝑚𝑖𝑧𝑒𝑑 𝑑𝑖𝑠𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛Ifeed = 4 A h = 50 Wm-2K-1

Design 2

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Choice of the final design

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h(Wm-2K-1)

Opt - 1A TPCB (°C)

Design - 1A TPCB (°C)

ΔT(K)

25 182.31 181.95 0.10

50 179.32 178.97 0.11

100 177.83 177.47 0.11

500 176.56 176.21 0.11

h(Wm-2K-1)

Opt - 2A TPCB (°C)


ΔT(K)

25 175.63 175.68 0.05

50 168.18 168.23 0.05

100 164.54 164.57 0.04

500 161.46 161.48 0.03

h(Wm-2K-1)

Opt - 3A TPCB (°C)


ΔT(K)

25 188.22 188.93 0.71

50 171.48 171.87 0.39

100 163.68 163.90 0.22

500 157.12 157.35 0.23

h(Wm-2K-1)

Opt - 4A TPCB (°C)


ΔT(K)

25 228.62 233.59 4.97

50 192.79 195.71 2.92

100 177.25 179.29 2.04

500 165.23 166.37 1.14

ΔT = TPCB,design - TPCB,Opt

Axial section of the finallychosen design.

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Conclusions

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• The topology optimization (SIMP) approach supported the developmentof a chassis for actively cooled downhole electronics.

• Two main design concepts were found and analyzed.

• A parametric study evaluated the sensitivity of the optimized topologiesto the boundary conditions.

• The final design was defined according to the optimization results andproved to perform very closely to the optimized systems.

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Thank you for the attention

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Extra slides

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27 November 2014DTU Energy, Technical University of Denmark14 20 October, 2015

COMSOL Multiphysics representation of the longitudinal section of the downhole tool (left side) and particular of the TEC device with the two plates and the semiconducting material layer highlighted in blue (right side).

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Governing equations

15

• Heat conduction 𝛻 −𝑘𝛻𝑇 = 𝑄𝑠𝑜𝑢𝑟𝑐𝑒 (1)

• Modified heat conduction 𝛻 𝑱𝑆𝑇 − 𝑘𝛻𝑇 = 𝑄𝐽𝑜𝑢𝑙𝑒𝐻𝑒𝑎𝑡𝑖𝑛𝑔 (2)

Boundary conditions

Convective heat flux (Tfluid, h)

Thermal insulation

Heat source(1 W)

TEC feed current Ifeed

Thermal (contact) resistance

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Cross-Check analysis

16

Evaluate the performance of the optimized designs at different boundary conditions

• The TEC feed current influencessignificantly the optimized design.But we can control it!

• An optimal feed current Ifeed,opt wasfound.

• Ifeed,opt varies with h and rangesbetween 2 and 3 A.

• The optimization process is negligiblysensitive to the well fluid convectionregime, at a given Ifeed.

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HTS electronics temperature vs. well fluid convective coefficient for four different systems, optimized for Ifeed = 2 A and h = 25, 50, 100 and 500 Wm-2K-1

.

R vs. well fluid convective coefficient, for different TEC feed currents. Different symbols refer to the different optimized design concepts.● = Design 1, ▲ = Design 2.

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HTS electronics temperature vs. TEC feed current for four different systems, optimized for Ifeed = 1, 2, 3 and 4 A, andh = 25 Wm-2K-1 (left side) and 50 Wm-2K-1 (right side).

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Characteristic curve of the finally designed electronics unit. The plot reports the performance of the cooling system as HTS electronics temperature vs. Convective coefficient and TEC feed current. The minimum HTS electronics temperatures for each operating condition are highlighted with a red line.

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𝐽′ =𝑁𝐼𝑓𝑒𝑒𝑑

𝐴𝑡𝑜𝑡=𝑁𝐼𝑓𝑒𝑒𝑑

𝐴𝑡𝑜𝑡∙𝑁𝐴𝑙𝑒𝑔

𝑁𝐴𝑙𝑒𝑔=𝐼𝑓𝑒𝑒𝑑

𝐴𝑙𝑒𝑔∙𝐴𝐵𝑖𝑇𝑒𝐴𝑡𝑜𝑡

= 𝐽 𝑥𝐵𝑖𝑇𝑒

𝑱′ ∙ 𝑆 = 𝑱 ∙ 𝑆′ → 𝑆′ = 𝑆 ∙ 𝑥𝐵𝑖𝑇𝑒

𝑘′ = 𝑘𝑎𝑖𝑟𝐴𝑎𝑖𝑟𝐴𝑡𝑜𝑡

+ 𝑘𝐵𝑖𝑇𝑒𝐴𝐵𝑖𝑇𝑒𝐴𝑡𝑜𝑡

= 𝑘𝑎𝑖𝑟 (1 − 𝑥𝐵𝑖𝑇𝑒) + 𝑘𝐵𝑖𝑇𝑒 𝑥𝐵𝑖𝑇𝑒

𝜎′ = 𝜎𝐵𝑖𝑇𝑒 𝑥𝐵𝑖𝑇𝑒 + 𝜎𝑎𝑖𝑟 𝑥𝑎𝑖𝑟 = 𝜎𝐵𝑖𝑇𝑒 𝑥𝐵𝑖𝑇𝑒

(Gordon 2002)

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𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑒: 𝑓𝑜𝑏𝑗 𝑇, 𝜌𝑑𝑒𝑠𝑖𝑔𝑛 =1

𝐴𝑃𝐶𝐵 𝛺𝑃𝐶𝐵

𝑇 𝑑𝛺𝑃𝐶𝐵 (3)

𝑐𝑜𝑛𝑠𝑡𝑟𝑎𝑖𝑛𝑡𝑠: 0 ≤ 𝜌𝑑𝑒𝑠𝑖𝑔𝑛 ≤ 1 (4)

𝒓 𝑇, 𝜌𝑑𝑒𝑠𝑖𝑔𝑛 = 𝟎 (5)

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𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑓𝑖𝑙𝑡𝑒𝑟: −𝑟2𝛻2 𝜌 + 𝜌 = 𝜌𝑑𝑒𝑠𝑖𝑔𝑛 (Lazarov 2011) (6)

𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝜌𝑖 =tanh 𝛽𝜂 +tanh(𝛽( 𝜌𝑖−𝜂)

tanh 𝛽𝜂 +tanh 𝛽 1−𝜂(Wang 2011) (7)

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𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝜌𝑖 =tanh 𝛽𝜂 +tanh(𝛽( 𝜌𝑖−𝜂)

tanh 𝛽𝜂 +tanh 𝛽 1−𝜂(Wang 2011) (7)

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Simulation results

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Simulation results

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p(η,β = 1)

p(η,β = 8)


COMSOL - Topology Optimization of an Actively Cooled … · 2015. 11. 20. · •The topology...

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